Dynamical systems
Graduate · Math
Syllabus focus
Standard syllabus · STEM / applied
Pricing calculator
Choose materials, tutoring, or both — or book a single session as needed. Customize your plan on the subscribe page.
$1,162 · Dynamical systems · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.
Topics typically covered
Standard syllabus
Flows and invariant sets
- Existence and uniqueness for ODEs; maximal intervals of solutions
- Flows, orbits, and invariant sets
- Limit sets, ω-limit sets, and attractors
- Lyapunov stability and Lyapunov functions
- Stable and unstable manifolds (local theory)
Bifurcation theory
- Parameter-dependent equilibria; structural stability (introduction)
- Saddle-node, transcritical, and pitchfork bifurcations
- Hopf bifurcation and limit cycle creation
- Normal forms and center manifold reduction (introduction)
- Codimension-two bifurcations (overview)
Discrete and symbolic dynamics
- Diffeomorphisms and return maps
- Smale horseshoe and symbolic dynamics
- Topological entropy (introduction)
- Period doubling cascade and universality
- Hamiltonian dynamics and KAM theory (overview)
STEM / applied
Applied dynamical systems
- Pattern formation in PDEs (reaction–diffusion, introduction)
- Celestial mechanics and n-body problems (overview)
- Neuronal dynamics and bursting models
- Epidemiological and ecological models with bifurcations
- Control of nonlinear systems near equilibria
Computation and analysis tools
- Numerical continuation and bifurcation software (AUTO, MatCont overview)
- Lyapunov exponent computation
- Delay differential equations (introduction)
- Random dynamical systems (introduction)
- Data-driven reconstruction of attractors (overview)
Notes
Topics reflect common graduate dynamical systems syllabi at US universities. Prerequisites include graduate ordinary differential equations and functional analysis basics.